POWER systems have high memory bandwidth and can take really large amounts of RAM. You're limited to what IBM sells then, but the x86 market at that top end also isn't that large and less standard: Many companies will sell you 1-2 socket servers with 64-512 GB RAM, but if you want >3 TB its getting thinner there too, so also less benefit from using x86. So POWER is an option there, if running Linux the difference for sysadmins isn't that large. And e.g. SAP supports it for their HANA in-memory database, so enterprises might buy them there. At the same time, lots of enterprise software doesn't run on them, so they're unlikely to fully migrate.
Then there's companies building their entire stack themselves and operate at a large enough scale that some porting costs are acceptable if it brings them a benefit. They'll always be looking at alternatives. Google is known to have experimented with POWER systems. Cloudflare afaik is using some ARM systems because they turned out to be the more efficient choice for them. At Google/Facebook/... scale, it's likely also a signaling tool when buying: Intel is more likely to give them what they want if there's a somewhat credible threat of them replacing part of their systems with non-Intel.
For Power vs x86 it probably matters a lot what type and scale of operations you're at. As far as I can tell x86 typically has the better price/performance ratio but then I think there are quite a few supercomputers that use Power so there must be some advantages (probably mostly I/O related).
Power CPUs tend to power either iSeries (latest iteration of AS/400 - System38 etc) systems or AIX based. The large AIX systems use lots of CPUs, cores and typically vPars - but I wouldn't call them supercomputers. Disk I/O is generally FC attached SAN, i.e. performance is achieved through off-loading. A typical SAN array contains gigabytes of caching memory, CPUs on each disk drive with yet more RAM and multiple optical FC links to each node.
Perhaps not but there are non-IBM Power systems available, such as those from Raptor, as well as IBM Power systems primarily intended to run Linux.
Also I think Google has looked into running Power systems, but I don't know that they have any in production.
Power supports virtualization from chip level which looks excellent. But heard little that company would like to transfer to power from x86.
Use Power RISC with AIX in established IBM user organisation that wanted to run Unix software so we ported existing software to AIX.
Use existing s390 system running several core systems, to run Unix partitions to deploy software already written for Unix in C.
I have never even heard of any company not already being an IBM account migrating to either of those systems. The capital and operating costs are typically far higher than for comparable performance x86 based deployments. Technical staffing is much harder still.
If this is true, this line may be another reply to my question.
One other consideration is that Intel chips come with closed source and completely opaque logic embedded in the silicon, such as the Intel Management Engine.
As I understand it Power is now a fully open source architecture and you can get a system with fully transparent firmware (at least if you buy a non-IBM system). Depending on your security needs and threat model that may be an advantage, but I doubt it's a significant enough concern for most companies to justify the lower price performance ratio.